# In a sports competition with 760 atheletes, the following pieces of information are true: 70% of the atheletes are runners, 40% of the men are not runners and 400 women are runners. How many women were there in total?

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Firstly, we must identify the two things that we need to work out our answer. They are: How many male runners there are, and how many male non-runners there are, as once we have these, the remaining value will be the number of female atheletes. (We know how many female runners there are (400), but alone, this does not help us.)

We know that 70% of the atheletes are runners, so, we can say that 532 of them are runners (because 70% of 760 is 532).

We can use this to work out that there are 132 male runners (because the number of runners - the number of female runners (532-400) = 132 male runners).

We know that 40% of the men are not runners, so, the number 132 only represents 60% of the male runners. Therefore, there are 220 male atheletes in total (132 divided by 6 = 22  so  22 multiplied by 10 = 220).

As we now have the total number of male atheletes, we can take this away from the total number of atheletes. Therefore, there are 540 female atheletes (760 - 220 = 540).

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